ABSTRACT

This chapter describes the method of solution of linear heat conduction problems by the application of various integral transforms, such as Fourier and Hankel transforms. These transforms remove the partial derivatives with respect to space variables and are equally attractive for both steady- and unsteady-state problems. The chapter discusses solutions of various linear heat conduction problems by the application of the classical method of separation of variables. It considers the extensions of the theory and introduces integral transforms in the semi-infinite and infinite regions. More fundamental and extensive treatment of the theory of integral transforms and their applications to the solution of heat conduction problems can be found. In solving a heat conduction problem by the application of an integral transform, the problem is first reduced to a much simpler problem consisting of an ordinary differential equation together with an initial condition for unsteady-state problems or with two boundary conditions for steady-state problems.